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Homogeneous Quaternionic Kahler Structures and Quaternionic Hyperbolic Space

Abstract

An explicit classification of homogeneous quaternionic Kahler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space \({\mathbb H}H(n)\) is characterised by admitting homogeneous structures of a particularly simple type. In the process we study the properties of different homogeneous models for \({\mathbb H}H(n).\)

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Correspondence to M. Castrillon Lopez, P.M. Gadea or A.F. Swann.

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Lopez, M., Gadea, P. & Swann, A. Homogeneous Quaternionic Kahler Structures and Quaternionic Hyperbolic Space. Transformation Groups 11, 575–608 (2006). https://doi.org/10.1007/s00031-005-1124-3

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Keywords

  • Nauk SSSR
  • Topological Group
  • Hyperbolic Space
  • Homogeneous Model
  • Homogeneous Structure